Motion segmentation is one of the main tasks in computer vision and is relevant for many applications. The optical flow (OF) is the input generally used to segment every frame of a video sequence into regions of coherent motion. Temporal consistency is a key feature of motion segmentation, but it is often neglected. In this paper, we propose an original unsupervised spatio-temporal framework for motion segmentation from optical flow that fully investigates the temporal dimension of the problem. More specifically, we have defined a 3D network for multiple motion segmentation that takes as input a sub-volume of successive optical flows and delivers accordingly a sub-volume of coherent segmentation maps. Our network is trained in a fully unsupervised way, and the loss function combines a flow reconstruction term involving spatio-temporal parametric motion models, and a regularization term enforcing temporal consistency on the masks. We have specified an easy temporal linkage of the predicted segments. Besides, we have proposed a flexible and efficient way of coding U-nets. We report experiments on several VOS benchmarks with convincing quantitative results, while not using appearance and not training with any ground-truth data. We also highlight through visual results the distinctive contribution of the short-and long-term temporal consistency brought by our OF segmentation method.